A Puzzle on Leap Frog Jumping

May 20th, 2015
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A jump move involves two adjacent pieces (men) along same row or same column • No cross-wise jump • After a jump, the man must land on a vacant position, and the man who is jumped over gets removed from the board • A piece can jump over only one piece in one move

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A Puzzle on Leap Frog JumpingA Puzzle on Leap Frog Jumping(With a surprising result) By N.D.PrabhakarBoard: Men placed at grid points A jump move involves two adjacent pieces (men) along same row or same column No cross-wise jump After a jump, the man must land on a vacant position, and the man who is jumped over gets removed from the board A piece can jump over only one piece in one moveRed , Yellow and Violet pieces can not jump Green can jump right over blue Blue can jump left over green Blue can jump up over yellow Blue can jump down over violetLevelsETC. above Level 3Level 2Level 1 Level 0 Level -1 ETC. belowProblems Designate one of the rows as Level 0, and rows above that as Levels 1,2,3, etc. You are allowed to place as many men as you need in any configuration of your choice in Level 0 and below (board potentially infinite) How many men would you need in order to reach a man to level k using leap frog jumping moves, for k=1,2,3, ?Reaching Level 1 Needs two menLevel 0Reaching Level 1 Blue piece jumps over green piece: green shown crossed outLevel 1 Level 0Reaching Level 2 Needs 4 menLevel 2 Level 1Level 0Reaching Level 2 1st move: Blue jumps up over greenLevel 2 Level 1Level 0Reaching Level 2 2nd move: Red jumps right over greenLevel 2 Level 1Level 0Reaching Level 2 3rd move: Red jumps up over blueLevel 2 Level 1Level 0Reaching Level 3 Needs 8 menLevel 3 Level 2 Lev

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